current-electricity Question 51
Question: Q. 4. Following circuit was set up in a meter bridge experiment to determine the value $X$ of an unknown resistance.
(a) Write the formula to be used for finding $X$ from the observations.
(b) If the resistance $R$ is increased, what will happen to balancing length? R&U [CBSE SQP 2018-19]
Sol. (a) $X=(100-l) R / l$
(b) Balancing length will increase in increase of resistance $R$.
[CBSE Marking Scheme 2018]
Q. 5. In a potentiometer arrangement for determining the emf of a cell, the balance point of the cell in open circuit is $350 \mathrm{~cm}$. When a resistance of $9 \Omega$ is used in the external circuit of the cell, the balance point shifts to $300 \mathrm{~cm}$. Determine the internal resistance of the cell.
A [ Delhi & O.D. 2018] Sol. Stating the formula 1
Calculating $r$
1
We have, $\quad r=\left(\frac{l_{1}}{l_{2}}-1\right) R=\left(\frac{l_{1}-l_{2}}{l_{2}}\right) R \quad 1$
$\therefore \quad r=\left(\frac{350-300}{300}\right) \times 9 \Omega$
$=\frac{50}{300} \times 9 \Omega=1.5 \Omega$
$1 / 2$
[CBSE Marking Scheme, 2018]
Short Answer Type Questions-II
Q. 1. (i) Write the principle of working of a metre bridge.
(ii) In a metre bridge, the balance point is found at a distance $l_{1}$ with resistances $R$ and $S$ as shown in the figure.
An unknown resistance $X$ is now connected in parallel to the resistance $S$ and the balance point is found at a distance $l_{2}$. Obtain a formula for $X$ in terms of $l_{1}, l_{2}$ and $S$.
A [O.D. I, II, III 2017]
Show Answer
Solution:
Ans. (i) Principle of metre bridge
1
(ii) Relation between $I_{1}, I_{2}$, and $S$
2
(i) The principle of working of a metre bridge is same as that of a balanced Wheatstone bridge.
Alternatively
When $\quad i_{G}=0$, then $\frac{P}{Q}=\frac{R}{S} \quad 1 / 2$
(ii)
$$ \frac{R}{S}=\frac{l_{1}}{100-l_{1}} $$
$1 / 2$
When $X$ is connected in parallel :
$$ \frac{R}{\left(\frac{X S}{X+S}\right)}=\frac{l_{2}}{100-l_{2}} $$
On solving we get, $X=\frac{l_{1} S\left(100-l_{2}\right)}{100\left(l_{2}-l_{1}\right)}$
1
[CBSE Marking Scheme 2017]
OR
Ans. (i)
Princeple of workeng of a metec beidge
The pecncipce is Wheatsen principce
If foce eescisances $D, Q, R$ ands aeconneded
in the whealstone beidge in the foclowing
manner, then at balanced condction, 2 cuerenc
in the galvanomelice is $2 e x 0$ on the
lescseance can be fornd:
(ii)
[II Q. 2. Draw a circuit diagram of a potentiometer. State its working principle. Derive the necessary formula to describe how it is used to compare the emfs of the two cells.
DiO.D. I, II, III 2015]
Ans. The circuit diagram of the potentiometer, is as shown here:
Working Principle :
The potential drop, $V$, across a length $l$ of a uniform wire, is proportional to the length $l$ of the wire. $1 / 2$ or, $\quad \mathrm{V} \propto l \quad$ (for a uniform wire) Derivation : From the figure, connect points 1 and 3 together with balance point at point $N_{1}$ where $A N_{1}=l_{1}$ Now connect points 2 and 3 together with balance point at point $N_{2}$ where $\mathrm{AN}{2}=l{2}$. $1 / 2$ We have,
So,
and
$E_{1}=k l_{1}$ $E_{2}=k l_{2}$
$$ \frac{E_{1}}{E_{2}}=\frac{l_{1}}{l_{2}} $$
$1 / 2$
